This soup is very forgiving (It just prefers that you actually ask for forgiveness), so you can "overcook" it if it's too runny. Just keep in mind that the carrots and celery will soften quite a bit also.
Just be sure to find a ham hock or a ham that is nitrate/nitrite free. That is one of the non-negotiables in our house. And it would ruin an otherwise perfectly good soup. Not that my kids would know.